Valhalla Legends Archive

Some responses on sci.physics newsgroup:

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The kinetic energy of the earth in its motion about the sun is roughly
9*10^26 Joules. So that much work would have to be done on the Earth to
bring its orbital motion to zero.

Bob Kolker
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Actually, it is more like 3*10^33 Joules.

So that much work would have to be done on the Earth to
>bring its orbital motion to zero.

The energy requirements are still the small part of it.  Momentum
needs to be conserved as well.  The linear momentum of the Earth, at
any given moment, is close to 2*10^29 Ns.  Now, the Saturn V first
stage engine (or, rather, cluster of engines) had thrust of about
4*10^7 Ns.  So, if you would build about a million of this babies
(never mind where the materials and labor are coming from), they would
have to run continuously for the next 150 million years (consuming an
amount of fuel 10 times larger than the Earth mass) to supply the
required impulse.

Mati Meron  
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Let's see. It's been a long time I played with planet but...

I think Uncle Al that if you just stop the motion of the earth it's
total mechanical energy E will still be negative, E<0 , due to just
the potential of the sun and it will again attain an elliptical orbit
around the sun but with some other radius and we will fry anyway.

It seems to me that in order to achieve what is called a "collision
path" or singular solution to orbit equations, one must increase the
total mechanical energy of the earth until it becomes E > 0. Then
earth will go into an open orbit (hyperbola or parabola) and depending
on eccentricity, mean and ecccentric anomaly, you may achieve a
collision course.

Contrary to common sense, of mayne not, the only way to increase the
total mechanical energy of the earth is by increasing its velocity.
Then bingo, 7 Bil morons fry to their extinction and the universe is
safe. Slowing it down does not do the job it seems, unless you also
supply an impulse to increase the total mechanical energy to positive
number.
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Nope.  It will be in a degenerate straight-line orbit
intersecting the Sun.

Hey, when you drop something on the Earth, does it go into
an elliptical orbit instead of hitting the ground?

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KISS - keep it simple, stupid.  Stop the Earth dead in its orbit, let
the sun do the rest of the work work, and get a default perfect hit in
the bargain (less Lens-Thirring frame dragging just before
touchdown).  Note the prior post regarding crush strength of the
Earth.

The original poster has not calculated corrected time to splatter nor
velocity at hit,

http://www.math.ubc.ca/~israel/m215/falling2/falling2.html

suggesting it was just noise not inquiry.

Uncle Al
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Depends on how close you are to the spheroid, dipshit.

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No it does not.  Stuff with zero orbital velocity falls straight down
vs. the fixed stars from any arbitrary height (ignoring wind)  If you
look locally you subtract out ground motion and allow for ~1 cm/sec
horizontal Coriolus acceleration varying with latitude.

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That's correct and I guess unless one is specific and uses the right
terms, like Uncle AL does, misunderstandings can arise.

The key word here is "fixed stars". If the answer is posed in this
context it's correct. However, in my answer I assumed an instantenuous
relative  fix of earth's velocity with respect to a moving sun. This
case is a bit more complicated. Actually, everything is in a constant
relative motion and fixing anything could be hard. This is also one of
the reasons that in practice there is no such a thing as a "straight
line path" and what one perceives as a straight line in a free fall is
actually an arc of some curve.

This is to say, for those with a little hearing problem, that is there
is accelative motion the free falling planet towards the sun will also
attain a non-zero orbital velocity. This automatically activates conic
sections as the solutions and it's not a degenerate line orbit any
longer.

Have an idea: let's try it.
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Mass of Earth is 5.976 * 10^24 kg.
50 years = 50 * 365.2422 * 86400 seconds = 1577846304 seconds
Velocity of Earth is 30 km/s.
Momentum of Earth is 30,000 m/s * 5.976 * 10^24 kg = 1.793 * 10^29 kg-m/s.

Force = momentum/duration = 1.793 * 10^29 kg-m/s / 1577846304 s
= 1.136 * 10^20 Newtons.

How one generates that force is an interesting issue.  I don't know
what your budget is. :-)

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All you have to do is change the orbit, by timing the
thrusts, to a highly elliptical one (think "comet") with
a closest approach that is within the sun's "atmosphere".
I'm assuming your customer would accept any form of
total fiery destruction, and doesn't require you to
actually plunge into the center of the sun.

          - Randy
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Something that I thought of while reading this post... What's the energy of a nuclear bomb and how much do we know about it's effect on our planet's course around the sun? Clearly it has tremendous energy, is it possible that this might have thrown us off course very slightly?

All this does not need to be done at once I am sure. We could slowly use up the energy as we get it to slow the Earth/push it...

I belive the energy of a nuclear weapon is far too little to throw the earth off course even the slightest bit.

E=mc^2.. just figure out the mass of whatever is reacting

If one were to take the energy released by an atomic bomb, and spread it out so the blast range covored the entire volume of the earth, the concentration of energy would significantly decrease. If you're worried about the Earth being thrown off course, consider that the gravitational pull of another planet/comet/etc will have a much more dramatic affect on Earth's acceleration and will last for a much longer period of time. Then you will see that it is not the spoon that bends, it is only yourself.

Very interesting! So you don't think we'll be able to blow ourselves into the sun even if we turn all the water on earth into a hydrogen bomb?

Quote from: Adron on September 18, 2003, 07:16 PMVery interesting! So you don't think we'll be able to blow ourselves into the sun even if we turn all the water on earth into a hydrogen bomb?

I was talking about a few hundred atoms, not all of our oceans. Then again, there isn't as much water as you might think on Earth: While the majority of Earth's surface is obscured by water, the depth is rarely more than a couple of miles. It probably would be enough energy to significantly alter the velocity of the Earth, and certainly would be enough to wipe out virtually all life. Furthermore, there is a theory that if enough nuclear reactions occur in close proximity, they can covor the activation energy of a nuclear reaction. This means that there's a good chanse you could completely nuke the entire Earth and possibly more.

Quote from: Camel on September 18, 2003, 07:08 PM
If one were to take the energy released by an atomic bomb, and spread it out so the blast range covored the entire volume of the earth, the concentration of energy would significantly decrease. If you're worried about the Earth being thrown off course, consider that the gravitational pull of another planet/comet/etc will have a much more dramatic affect on Earth's acceleration and will last for a much longer period of time. Then you will see that it is not the spoon that bends, it is only yourself.

It doesn't matter where you do it, as long as you can change the momentum of the earth.  It can be in one spot, as long as you can change the momentum.

Quote from: iago on September 18, 2003, 08:55 PMIt doesn't matter where you do it, as long as you can change the momentum of the earth.  It can be in one spot, as long as you can change the momentum.

Yes, iago.  It seems so simple.  Any reduction of the Earth's orbital velocity should be enough.  Remember that the Earth is always falling into the Sun.  Currently the rate it is falling is offset by its orbital velocity.  The falling is caused by gravity and the orbital velocity measures its momentum.  Remove or reduce the momentum and the Earth's falling overtakes the balance, and it appears to "start falling" into the Sun.

It might be easier to make an impact on the moon that would cause the earth to change orbit.

Quote from: Thing on September 18, 2003, 10:13 PM
It might be easier to make an impact on the moon that would cause the earth to change orbit.

Hmm, I don't see how exerting the force on the moon to cause the effect would need less energy.  Whether the force is applied directly to the Earth, or via proxy through the moon, the actual force required would be the same.

Well, if the moon's orbit was changed it would be consistantly putting a force on the earth because of the changed orbit, but if you did it to the earth it would only be changed by the initial force.. although Grok might be right, it's an interesting question

Quote from: iago on September 18, 2003, 10:29 PM
Well, if the moon's orbit was changed it would be consistantly putting a force on the earth because of the changed orbit, but if you did it to the earth it would only be changed by the initial force.. although Grok might be right, it's an interesting question

Shouldn't the energy required to change it be constant no matter where we apply it? We may be able to save energy by picking a clever elliptical orbit that touches the sun instead of going for a straight hit though.

Well, it seems like it should be comparable to pushing a ball on a flat surface or down an incline.  You're providing the same force, but in one situation the force ends up with a sustained force... again, this could be wrong, though

Quote from: iago on September 19, 2003, 08:43 AM
Well, it seems like it should be comparable to pushing a ball on a flat surface or down an incline.  You're providing the same force, but in one situation the force ends up with a sustained force... again, this could be wrong, though

Hmm, to me that sounds more like the choice of what path to have the earth follow - linear approach or some kind of spiral. Just applying a certain force to the moon should move the moon a bit, but what you in reality are moving is the center of gravity of the system consisting of the moon and the earth. You'll change the orbits in which the moon and the earth rotate around each other, and whether you choose to move the moon or the earth I think you'll have the same effect on the center of gravity of the system.